Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	188×	body	80	valid
5.0ms	27×	body	1280	valid
4.0ms	20×	body	2560	valid
4.0ms	256×	pre	80	true
1.0ms	9×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.1b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

26.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
30.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
54.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
62.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	297	951
1	884	898
2	2732	885
3	5001	883

prune526.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.0b	(/ x (fma (* 4.0 p) p (* x x)))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`fma-def`
9×	`times-frac`
7×	`unpow-prod-down` `cube-prod`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `frac-2neg` `unpow3` `div-exp` `clear-num` `sum-log` `sum-cubes` `div-inv` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

78.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.0ms	(/ x (fma (* 4.0 p) p (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
54.0ms	(/ x (fma (* 4.0 p) p (* x x)))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	285	751
1	1103	692
2	5001	688

prune515.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.7b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

3.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
35.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
56.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	407	966
1	1757	881
2	5001	845

prune308.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.9b

localize17.0ms

Local error

Found 4 expressions with local error:

3.2b	(cbrt (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`cbrt-div`
1×	`cbrt-prod` `pow1/3` `associate-*r/` `un-div-inv`

Counts

4 → 64

Calls

4 calls:

10.0ms	(cbrt (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	176	558
1	612	526
2	2363	518
3	5001	518

prune313.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.9b

regimes111.0ms

Accuracy

0% (0.2b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	29
1	28	29

end0.0ms

sample835.0ms

Algorithm

intervals

Results

205.0ms	6013×	body	80	valid
193.0ms	869×	body	2560	valid
107.0ms	8000×	pre	80	true
106.0ms	602×	body	1280	valid
45.0ms	314×	body	640	valid
14.0ms	137×	body	320	valid
5.0ms	65×	body	160	valid